We provide empirical evidence that deviations from uncovered interest rate parity (UIP) display significant nonlinearities, consistent with theories based on transaction costs or limits to speculation. This evidence suggests that the forward bias documented in the literature may be less indicative of major market inefficiencies than previously thought. Monte Carlo experiments allow us to reconcile these results with the large empirical literature on the forward bias puzzle since we show that, if the true process of UIP deviations were of the nonlinear form we consider, estimation of conventional spot-forward regressions would generate the anomalies documented in previous research.